Unlike other games, none of these achievements are given to you without a fight. You probably won't get most of them on your first attempt. You probably won't get most of them at all, but that's why they're called achievements. They will require serious patience, numerous playthroughs, a bit of luck and a lot of skill.

Note that while only one achievement explicitly requires a second, third, or fourth player, some are easier with extra players helping you out.

Beat the Tutorial

Pretty easy, actually. The hardest part is realising that paying ten bucks for an awesome game is a good decision. Well done for not being a miserly old cheapskate.

All you have to do is complete the Tutorial cave. It's exactly the same every time, and there aren't too many hazards.

• Follow the prompts when you see them and don't go out of your way to collect the treasure - You only need to get to the exit, and there's nothing you particularly need from the shop.

Reach the Jungle.

Relatively simple.

To unlock this, you need to complete the first four levels, getting to the tunnel where the Jungle starts. Once you're comfortable with the game, you should be able to get this far without too much trouble, but it may take you a few deaths.

• If all you want to do is unlock the achievement, you can be a bit more liberal with your bombs and ropes than you would usually be, as you don't need to worry about saving them for later.
  
  
• Most of the enemies in the Mines are fairly easy to avoid. Just look out for arrow traps and don't go running onto spikes.
  
  
• Don't bother with the Golden Idols. The boulders have a nasty tendency to go rolling into shops, and it's not worth risking angering the Shopkeepers for money you're probably not going to spend. Just focus on getting to the exit.

Reach the Ice Caves.

Doable.

This achievement requires you to complete the Jungle. Same deal as the mines, you just need to survive these 4 levels and get to the tunnel to the the Ice Caves.

The Jungle is trickier to navigate than the caves. The terrain is more difficult to overcome, as there tend to be more long falls and tall obstacles, not to mention all the fast enemies and instant-death traps.

• You can get this achievement if you take the shortcut to skip the mines, but you may wish to play through those levels anyway to earn items and Damsel kisses that will help you survive here.
  
  
• Just get to the exit. You don't need treasure. See that Crystal Skull? Keep walking.
  
  
• There are lots of enemies that you can sacrifice in the Jungle, but don't get greedy. You don't want to get cornered by the Ghost, and you're more likely to survive if you avoid enemies altogether, rather than attacking them for sacrifices.
  
  
• Don't take your chances with Tiki Traps. If it's in your way, bomb it. Don't try to clamber over it, blow it up or find a different route.
  
  
• If an item falls down a narrow pit next to one, don't try to retrieve it.

Reach the Temple.

Tough, but you'll manage it.

You need to complete the Ice Caves by getting to the tunnel to the Temple.
The Ice Caves are quite a lot harder than the first two areas as the enemies and the environment are a lot more dangerous.

The skills needed to beat the Ice Caves are a bit different than usual, as the terrain is so different. You actually need to learn to play a different game to be successful here.

• It helps a lot if you have the jetpack (or cape) and the spike shoes, so you actually have a better chance of succeeding if you take the time to play through the previous levels, instead of taking the shortcut straight here.
  
  
• Play conservatively. Take your time. Don't worry too much about the Ghost, these levels don't actually take much time to complete - the difficulty comes from all of the instant-death situations you can wind up in. There's actually very little standing in the way between you and the exit, so choose your route carefully, avoiding those Yeti and UFOs.
  
  
• Don't enter the Mothership. It always appears on level 3-4, but finishing through that exit means you'll have to survive the Bonus level, and then complete a new level 3-4 as well before you get the achievement. What's the point?
  
  
• Don't stick around trying to kill enemies, everything you'll find here is pretty tough and it's not worth the time wasted.

Complete the game.

It will take many many tries, if you're even good enough at all. If you really want it, you'll get there one day. You just have to BELIEVE.

You get this achievement for completing the three levels of the Temple and defeating Olmec to win the game.

Obtain 500,000 gold.

Pretty difficult.

You need to earn $500,000 in one life. Once you reach half a million, the achievement is given to you.

• You need to get good at the game before you try this. You'll earn more money when you are able to survive for longer, so if you can't make it past the first few levels you're not going to be able to grab this much treasure before you die.
  
  
• Rather than avoiding all shops and never spending any money, plan ahead and don't be afraid to make investments.
  
  
• For example, bombs, when used effectively, earn you much more money than they cost. A jetpack will allow you to get treasure that would ordinarily be out of reach, and also helps you move faster, so you can grab more gold before the Ghost appears to shoo you out of a level.
  
  
• Conversely, don't spend money on items that won't pay off. Spike shoes won't win you any cash and there's no point shelling out for a Shotgun when you can get one for free in a Restless dead level. Even a Tiki Man's Boomerang is an adequate weapon if used skillfully.
  
  
• If you manage to get to the City of Gold, you practically have this achievement in the bag. Gather as many bombs as you can and trash the place.

Reach the City of Gold.

Manageable.

Reaching the City of Gold requires you to collect a few items in each world: The Ankh, the Headjet and the Scepter.

In the City of Gold you can find the Book of the Dead. This book allows access to Hell. Once you grab the book Anubis II appears. If you continue on to 4-4 without killing him he will follow you into the Olmec boss fight.

The video below explains everything.
https://www.youtube.com/watch?v=OskIT96LRdg

Obtain the Ankh.

Manageable.

Acquire the Ankh from the Black Market.

• If you don't have the $50,000 needed to buy the Ankh and don't care about survival, you can simply steal it. You will be given the achievement even if you don't make it two steps out of the shop before you're gunned down.

Complete the game without using shortcuts.

Manageable.

You must complete all 16 levels of the game in one run, starting from the main entrance to the mines and defeating Olmec.

• It is not necessary to complete Hell to earn this achievement, so don't risk your life to get to the City of Gold and taking the Necronomicon. You may still wish to buy the Ankh from the Black Market, using it as an extra life in case you get killed.

Complete the game in under 8 minutes. No shortcuts.

Very hard.

https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=172265778

Play Adventure Mode 1000 times.

It's a grind, but doesn't take skill or luck to complete.

This achievement requires that you play adventure mode 1000 times.
Walking through any door in the gateway cave (be it the entrance to the Mines or a shortcut) counts as one 'play'. You can keep track of how many times you've played by viewing your Deaths/Wins in the Player Stats screen on the main menu.

• This Achievement isn't difficult per se, it just requires that you have a lot of time and enjoy Spelunky enough not to get bored half way through. You'll probably get this after a moderate amount of time playing the game. Maybe about a month or two if you play somewhat often.
  
  
• You can 'grind' for this achievement by simply starting a game and then killing yourself with the 'End Adventure' option in the pause menu, but since you can't technically 'fail' at this challenge you may as well do it in a way that isn't mind-numbingly boring, even if it takes a bit longer.
  
  
• It also helps assuage the frustration of dying repeatedly if you know that your misfortune is at least contributing towards something.

Complete the game the hard way.

High.

To make it to Hell you will have to collect many different items in each world and kill Olmec a specific way. The video below explains everything.
https://www.youtube.com/watch?v=OskIT96LRdg

Complete 50% of the journal.

Complete 100% of the journal.

Hard, man. Hard. You've gotta be really good.

This achievement requires that you complete the journal by collecting every entry in Places, Monsters, Items and Traps.

It's significantly harder than getting the halfway achievement, as you'll need to go through every level (even Hell), at least to the point where you get killed by the final boss. As a result, you'll get many of the other achievements before you get this one, including Ironman and City of Gold just to get this far.

Rescue 10 or more damsels in one game.

Kill 12 or more shopkeepers in one game.

Shopkeepers are merciless enemies and have zero tolerance for provocation. This will require some practice.

For details on Shopkeeper behaviour and how to fight them, see this article on the Spelunky Wiki[spelunky.wikia.com] or the following guide:
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=171072905

Complete the game without collecting any treasure. No shortcuts.

Hard.

Defeat Olmec without collecting any treasure.

• This achievement becomes unavailable as soon as you collect any treasure in the run, even if you spend it before defeating the final boss.
  
  
• If you can't jump over it, you can use your whip to move treasure out of the way.
  
  
• You can use the Shield to avoid accidentally running over treasure, crushing pieces against walls to avoid picking them up. Be careful not to drop down on top of it however.

Complete the game with at least two players alive. No shortcuts.

Depends.

This video demonstrates how you can solo this Achievement.
https://www.youtube.com/watch?v=lAoB6xAhs3w

Win the kapala from Kali.

Easy enough.

Acquire the Kapala from Kali by earning 16 favor in one run.

• The fastest and simplest way of doing this is by sacrificing two living Damsels, which earn you eight favor points each. The first sacrifice will earn you a useful item, and the second will grant you the incredible powers of the Kapala as well as the achievement.
  
  
• Finding an Altar in the Ice Caves is also a blessing, especially if you have a jetpack. Yetis are plentiful and earn a decent amount of favor when sacrificed alive, so you can potentially gather enough favor for the Kapala in a single level.

Rescue all 8 hidden characters.

This achievement requires that you unlock eight hidden characters. Some are harder to unlock than others, and the hardest requires that you complete Hell.

For more details on how to unlock characters, see this guide:
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=167824186

This guide is mostly based on the excellent Spelunky Wiki[spelunky.wikia.com] (notably the Achievement Help[spelunky.wikia.com] page) and thus available under CC-BY-SA[www.wikia.com]. Kudos to them.

Though this guide lists all Achievements and how to get them, I still consider it incomplete. Some sections, like The City of Gold and Ironman could use more details. I will link appropriate Steam Guides as soon as they are available.

Know of a good guide or video? Link it in the comments below.